mmm4444bot: Interesting. It could be that there is an error in the exercise and what you gave is what was intended (in your final quadratic mean, you forgot r). However, it is also an odd coincidence that 2π is about 6, which is the solution for 2 times the area.

Subhotosh Khan: There is no reference to concentricity. In an exercise that says to find a minimum volume, there is no reference to differentiation, but that is the way to the solution.

Subhotosh Khan and stapel: I tried to attach a drawing I made with Paint as to what I mean about concentric elements. It let me choose what file to upload, but there was no "OK", or "Continue" or "Upload" or anything to complete the attach.

To describe it, imagine a circle whose radius is R. A concentric element would be inside said circle with radius r and a width of dr. The sum of all dr would be R. Again, this is only a guess as to some relationship that I proposed that might lead to the solution of twice the area, unless mmm4444bot is correct about an error in the exercise..

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